GPS speed on the wrist or elsewhere on the body contains a great deal of noise, but has a very small bias error, i.e. a systematic error. The accuracy of a GPS speed signal shown on the frequency level is very close to direct current DC and diminishes rapidly as the frequency increases, as shown in FIG. 1 with the aid of curve 1. The measurement accuracy can be improved using traditional signal filtering methods, or with the aid of GPS-Doppler measurement. Nevertheless, at a typical measurement frequency of 1 Hz, and with the person walking, the noise in a purely GPS-based speed measurement can be in the order of as much as 20-30%, compared to the signal.
On the other hand, the speed estimated from an acceleration sensor on the wrist or elsewhere on the body contains less noise, so that its accuracy will remain good when the frequency increases, up to a certain limit. However, there can be even a large bias error in speed measured in this way. Accordingly, the best accuracy of speed estimated from acceleration is poorer than when using GPS. The accuracy in the frequency plane of speed measured with the aid of an acceleration sensor is typically according to curve 2 of FIG. 1.
However, in practice the aim would be to obtain speed accuracy on the frequency level according to curve 3 of FIG. 1, i.e. accurate measurement over a wide range. The aim is also to create measurement that reacts sufficiently well to changes in the state of motion, but poorly to error sources relating to the measurement event itself.
Similar problems also relate to the GPS-based determining of altitude and vertical speed. Further, a somewhat similar problem also relates to the determining of altitude information with the aid of a pressure sensor, though in this case the errors are caused by slow (low-frequency) variations in atmospheric pressure.